What would be a good buy for lets say 5k (no more money available as I am a father now (lol)). On a scientific proven level, what should we buy to get the most out of it?
Starting with scientifically proven speakers, you need to purchase the brands/models that are designed that way. I know of only one brand where controlled listening tests backed by millions of dollars of published peer-reviewed research: Harman. That is the parent company and specific brand is Revel and some of their JBL line (e.g. M2 and 3867). No other company designs products from ground up that way. No Revel speaker for example is allowed to be released regardless of technical merit until it beats its competition in double blind tests.
Fortunately they have excellent products from bookshelf on up to full tower. See the Performa 3 for example:
http://revelspeakers.com/revel-performa3.html. Since speakers don't obsolete hardly at all, I would put at least half of your budget there.
Next you need a way to deal with your room. Revel/Harman speakers are designed to have similar off-axis response to on-axis. This means the sound you get above a few hundred hertz, is almost independent of the room you put them in.
Below a few hundred hertz, the room dominates the sound you hear, not the speaker. Since we put some 25% emphasis on bass when it comes to fidelity, it is essential to optimize that. No system regardless of price has proper bass without this. Again, the room is controlling this, not the speaker, not the amp, not the DAC, not the cable, etc. And it is very simple physics of sound waves combining.
Free options for above include measuring your room (see my tutorial here:
https://audiosciencereview.com/foru...om-measurement-tutorial-for-dummies-part-1.4/) and then optimizing your seating positiona and speakers. But that still leaves bass issues even in best circumstances. You need electronic correction for best results ("Room EQ"). I plan to write a tutorial on doing this manually but there are automated systems out there. If you are using a PC as a source, Dirac Live is a turnkey solution but pricey (about $1000 from what I recall). That is what I use on my 2-channel system.
Speaking of source, I trust you have already gotten on the bandwagon of streaming music from a computer/NAS/server. All of this fidelity talk is nonsense if convenience is not there. Get Tidal subscription while you are at it and enjoy more music than you can for hundred lifetimes for the price one CD a month! I use Roon software plus Tidal and Dirac and life is great.
For amplifier, get something with lots of power. If there is anything that can make amps sound different is when they run out of power. Class-D amps have gotten good bringing the price of such a solution way down. If you can though, make sure to seek out reviews as Class-D amps interact with the load/speaker, resulting in potentially colored sound (in high frequencies).
For DACs, the Topping D30 remains my favorite at just $129 shipped in US:
https://audiosciencereview.com/forum/index.php?threads/topping-d30-dac-measurement-and-review.2016/
These are all decisions and tips that can be heavily defended with audio science/engineering.